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On the positive mass, Penrose, and ZAS inequalities in general dimension. (English) Zbl 1260.53127

Bray, Hubert (ed.) et al., Surveys in geometric analysis and relativity. Dedicated to Richard Schoen in honor of his 60th birthday. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-230-5/pbk). Advanced Lectures in Mathematics (ALM) 20, 1-27 (2011).
Author’s abstract: “After a detailed introduction including new examples, we give an exposition focusing on the Riemannian cases of the positive mass, Penrose, and ZAS inequalities of general relativity, in general dimension.”
This paper contains a survey of several types of Riemannian \(n\)-manifolds which may be isometrically embedded in \((n+1)\)-dimensional space-times, \(n\) greater or equal to three.
Reviewer’s remark: In the case of “asymptotically flat manifolds”, the reviewer might wish to know why the definition “is easily generalized to allow for more than one asymptotically flat end”; but if he wants to deal with this subject area intensively he will find a lot of references.
For the entire collection see [Zbl 1245.00026].

MSC:

53C80 Applications of global differential geometry to the sciences
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C20 Global Riemannian geometry, including pinching
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